This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 11-076585, filed Mar. 19, 1999, the entire contents of which are incorporated herein by reference.
The present invention relates to a pattern writing technique for writing the pattern of an LSI or the like, and, more particularly, to a pattern writing method and pattern writing system which write a pattern by correcting a proximity effect.
In writing the pattern of an LSI using an electron-beam writing system, the backward scattering of the beam causes a so-called proximity effect. The proximity effect changes or degrades the size precision of a resist depending on, for example, the designed size of the pattern or the presence of a peripheral pattern.
A dose correction method is one way of correcting this proximity effect. This method corrects an error by changing the dose of the electron beam in accordance with the target position and has been used in directly writing a pattern on a wafer. In this method, the optimum dose is computed by software using a general-purpose computer provided outside an EB (Electron Beam) system. At this time, the results of the calculation or the like are checked outside the EB system after which data on the dose of the electron beam is input to the EB system to be used in writing a pattern.
The recent ever-increasing integration of LSI patterns makes the influence of the proximity effect greater, so that the technology of proximity effect correction becomes more and more essential. For instance, the dose of the electron beam that is effectively emitted on the resist is the amount of forward scattering electrons plus the amount of backward scattering electrons which is the beam reflected at the surface of the substrate to be processed. Therefore, proximity effect correction should consider the amount of backward scattering electrons.
One conventional way of correcting proximity effect in an electron-beam writing method is to segment the writing area of an LSI pattern into small regions, acquire the area of each small region, obtain the amount of backward scattering electrons based on that area of each small region and then acquire the optimum dose from this amount of backward scattering electrons (see, for example, Takayuki Abe et al. xe2x80x9cRepresentative Figure Method for Proximity Effect Correction [ii]xe2x80x9d Japanese Journal of Applied Physics Vol. 30, No. 11A, November, 1991, pp. 2965-2969).
The present inventors discovered through intensive studies that a peculiar error occurs when there are repetitive patterns whose pitch slightly differs from the side length of each small region in the pitch direction. This problem is inherent not only to electron beam writing but also to ion beam writing.
Accordingly, it is an object of the present invention to provide a pattern writing method and pattern writing system which can implement highly-precise proximity effect correction even when there are repetitive patterns whose pitch slightly differs from the side length of each small region in the pitch direction, and can thus contribute to improving the writing precision.
To achieve the above object, a pattern writing method according to the first aspect of this invention comprises the steps of:
dividing a region of a to-be-exposed substrate on which a pattern is to be written into a plurality of small regions;
relatively shifting coordinates of the pattern and the plurality of small regions n times (n: an integer equal to or greater than 2) within a shift range whose absolute value is smaller than a size of the plurality of small regions and computing an area of at least one portion of the pattern located in each of the plurality of small regions in each of the n times, thereby acquiring n pieces of area data;
computing an optimum dose for the at least one portion of the pattern based on the n pieces of area data; and
writing the pattern on the to-be-exposed substrate based on the optimum dose.
The following are preferable embodiments of this pattern writing method.
The optimum-dose computing step includes the step of computing an amount of backward scattering electrons based on the n pieces of area data.
The backward-scattering-electrons-amount computing step includes the step of computing the amount of backward scattering electrons by convolution based on the n pieces of area data and spreading of backward scattering.
The backward-scattering-electrons-amount computing step computes the amount of backward scattering electrons by an equation given below based on the area:
U(x)=∫S(xxe2x80x2)exp{xe2x88x92(xxe2x80x3xxe2x80x2)2/xcex7"sgr"b2}dxxe2x80x2
where U(x) is the amount of backward scattering electrons, S(xxe2x80x2) is the area, x and xxe2x80x2 are coordinates and "sgr"b is spreading of backward scattering.
The optimum-dose computing step computes the optimum dose by an equation given below based on the amount of backward scattering electrons:
D(x)=C/(xc2xd+xcex7U(x))
where D(x) is the optimum dose, xcex7 is a ratio of an exposure amount sensitive to a resist by forward scattering electrons to that by backward scattering electrons and C is a constant.
The optimum-dose computing step includes the steps of:
multiplying each of the n pieces of area data by 1/n and then adding resultant areas together to thereby acquire an added area; and
computing the optimum dose based on an amount of backward scattering electrons acquired based on the added area.
The optimum-dose computing step may include the steps of:
adding n amounts of backward scattering electrons respectively obtained based on the n pieces of area data to thereby acquire an added amount of backward scattering electrons; and
computing the optimum dose by multiplying the added amount of backward scattering electrons by 1/n.
The plurality of small regions are rectangles of a same size which satisfy
0xe2x89xa6dxxe2x89xa6lx
and
0xe2x89xa6dyxe2x89xa6ly
where lx is a length of x-axial sides, ly is a length of y-axial sides perpendicular to the y-axial sides, dx is an absolute value of an amount of a relative shift of each of the plurality of small regions in an x-axial direction and dy is an absolute value of an amount of a relative shift of each of the plurality of small regions in a y-axial direction.
The total of absolute values of amounts of n relative shifts is equal to or smaller than lx/2 in the x-axial direction and is equal to or smaller than ly/2 in the y-axial direction.
In this pattern writing method, n is an even number and a total of the amounts of the n shifts in at least one of the x-axial direction and the y-axial direction is zero.
A pattern writing system according to the second aspect of this invention comprises:
means for dividing a region of a to-be-exposed substrate on which a pattern is to be written into a plurality of small regions and computing an area of a pattern segment located in each of the plurality of small regions;
means for relatively shifting coordinates of the pattern and the plurality of small regions within a range smaller than a size of the plurality of small regions;
means for accumulating the area of the pattern segment located in each of the plurality of small regions acquired for each shift, small region by small region; and
means for computing an optimum dose based on the accumulated area of the pattern segment in each of the plurality of small regions.
It is desirable that the optimum-dose acquisition means includes convolution means for computing an amount of backward scattering electrons based on the accumulated area of the pattern segment in each of the plurality of small regions.
A pattern writing system according to the third aspect of this invention comprises:
a figure division section for dividing a region of a to-be-exposed substrate on which a pattern is to be written into a plurality of small regions;
an area accumulation section for relatively shifting coordinates of the pattern and the plurality of small regions within a range smaller than a size of the plurality of small regions, computing an area of a pattern segment located in each of the plurality of small regions shift by shift, and accumulating the area of the pattern segment located in each of the plurality of small regions acquired for each shift, small region by small region;
a convolution section for computing an amount of backward scattering electrons based on the accumulated area of the pattern segment in each of the plurality of small regions;
a dose calculation section for computing an optimum dose based on the amount of backward scattering electrons for each of the plurality of small regions; and
an electron optics system for writing a pattern on the to-be-exposed substrate based on the optimum dose.
In the pattern writing systems according to the second and third aspects of this invention, it is desirable that the plurality of small regions are rectangles of a same size; and
the shift means or the area accumulation section should carry out relative shifts in such a way as to satisfy
0xe2x89xa6dxxe2x89xa6lx
and
0xe2x89xa6dyxe2x89xa6ly
where lx is a length of x-axial sides, ly is a length of y-axial sides perpendicular to the y-axial sides, dx is an absolute value of an amount of each of the relative shifts of each of the plurality of small regions in an x-axial direction and dy is an absolute value of an amount of each of the relative shifts of each of the plurality of small regions in a y-axial direction.
It is desirable that the shift means or the area accumulation section performs the relative shifts in such a way that a total of absolute values of amounts of the relative shifts is equal to or smaller than lx/2 in the x-axial direction and is equal to or smaller than ly/2 in the y-axial direction.
It is further desirable that the shift means or the area accumulation section performs the relative shifts in such a way that a total of the amounts of the relative shifts in at least one of the x-axial direction and the y-axial direction is zero.
According to this invention, a pattern writing method acquires the area of a pattern segment located in each of a plurality of small regions obtained by dividing a region on which an LSI pattern is to be written, small region by small region, and writes a pattern based on an optimum dose calculated based on this area. This method employs a scheme of shifting pattern segments and averaging the accumulated area, so that even when the pitch of repetitive patterns slightly differs from the side length of each small region in the pitch direction, a peculiar error does not occur, thereby ensuring highly-precise proximity effect correction and contributing to improving the precision of writing an LSI pattern.
Additional objects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out hereinafter.